Question

Calculate each unknown side length. Round your answer to the nearest tenth.

Answer 1

1. y=12.6 units

2. x=25.30 units

3. x=5.70 units, y=11.50 units

4. x=4.10 units, y=11.50 units.

Step-by-step explanation:

In all cases, apply the Pythagorean relationship where the sum of the squares of the sides equals the square of the hypotenuse.

a²+b²=c² where a and b are the sides, and c is the hypotenuse

1.

In this question;

First find b, where c=5  and a is 4

a²+b²=c²

4²+b²=5²

16+b²=25

b²=25-16=9

b=√9=3 units

To get y apply the formula now where c=13 and b=3

y²+3²=13²

y²+9=169

y²=169-9=160

y=√160=12.6 units.

2.

The triangle with a hypotenuse of 20 in is a right-isosceles triangle.

In this triangle apply the sine of an angle law to get the height of the triangle where the angle is 45°

Sin 45°=opposite side length/hypotenuse length

sin 45°=h/20

h=20*sin 45°=14.10 units

Use the height to find the side length for the small triangle when now c=18 and b=14.10

a²+b²=c²

a²+14.10²=18²

a²=18²-14.10²

a²=11.20

Now x= 11.20+14.10 =25.30 units

3.

In this case first find length of x given b=4 and c=7

a²+b²=c²

x²+4²=7²

x²+16=49

x²=49-16

x²=33

x=√33 =5.70 units

Now find y using a=x=5.70 and b=6+4=10

a²+b²=c²

5.70²+10²=c²

132.49=c²

√132.49=c

11.50=c=y

y= 11.50 units

4.

First find x where b=8 and c=9

x²+8²=9²

x²=9²-8²

x²=17

x=√17 =4.10 units

Now find y where b=8, a=(4.10+4.10)=8.20 ----because you have two equal sides

a²+b²=c²

8.20²+8²=y²

131.24=y²

√131.24=y

11.50 units = y

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Pythagorean relationship application:brainly.com/question/9319790

Keywords: calculate, unknown sides, tenth

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